Calculation of flow properties and end effects in field-flow fractionation channels by a conformal mapping procedure.
Calculation of flow properties and end effects in field-flow fractionation channels by a conformal mapping procedure.
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通过共形映射程序计算场流分级通道中的流动特性和末端效应。
DOI：
10.1021/ac00125a010
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发表时间：
1986
影响因子：
7.4
通讯作者：
Giddings,JC
中科院分区：
文献类型：
--
作者：
Williams,PS;Giddings,SB;Giddings,JC
在讨论了场流分馏（FFF）通道中近程和长程流动不均匀性的作用之后，描述了两种长程现象，即边缘效应和末端效应。结果表明，端效应可以用二维流动方程来处理，尽管这些方程仅严格适用于无限薄通道的极限，其中边缘效应不显著。利用Schwarz-Chrlstoffel变换（一种保角映射技术）将通道末端的困难边界条件简化为易于处理的形式。数值程序被开发来计算等势曲线，流动流线，最后从这个流动演变成新月形的样品剖面。数值计算了板高对区域畸变的贡献，并与近似理论的结果进行了比较。本文给出了一些图表来说明这些独特的流效应。最后，计算出的区域轮廓与透明通道中观察到的染料的新月形带很好地吻合。在基于流动的分离系统中，如色谱和场流分馏（FFF），柱效率和分辨率密切依赖于这些系统中的流动剖面。流动不均匀性一直存在，并对分离性能产生重大影响。流动中的短程不均匀性导致非平衡带展宽，而远程不均匀性导致区域畸变和附加展宽。最佳性能需要仔细考虑这两类流型效应。在FFF中，注意力几乎完全集中在存在于两个主要通道壁之间的薄间隙中的抛物线或近抛物线流动剖面上。不仅分离过程本身是由这个（短程）剖面控制的，而且非平衡效应（带宽的主要来源）也与剖面细节直接相关。直到最近，理论工作才集中在FFF中的远程流动不均匀性上（1,2）。这些不均匀性在这里被认为是速度差间隔太大，以至于在运行过程中扩散无法在不均匀点之间有效地来回传递样品颗粒。由于液相扩散缓慢，1毫米或更大的距离通常必须被认为是长距离。FFF通道的宽度（从一个边缘到另一个边缘的跨度）上的流动不均匀性，通常涉及一厘米或更多的距离，显然属于长程类。确定了沿宽度尺寸流动不均匀性的两个来源。第一次发生在海峡
Following a discussion of the roles of short-range and longrange flow nonuniformities in field-flow fractionation (FFF) channels, two long-range phenomena, consisting of edge ef-fects and end effects, are described. It is shown that end effects can be treated by two-dimensional flow equations, although these are rigorously applicable only in the limit of Infinitely thin channels where the edge effects are Insignifi-cant. The Schwarz-Chrlstoffel transformation, a conformal mapping technique, is Invoked to reduce the difficult boundary conditions of the channel endpieces to a tractable form. Numerical procedures are developed to calculate equlpoten-tial curves, flow streamlines, and finally the crescent-shaped sample profiles that evolve from this flow. The plate height contribution of the zone distortion is calculated numerically and compared to the result of an approximate theory of this effect. A number of diagrams are presented to Illustrate these unique flow effects. Finally, calculated zone profiles are shown to be in good agreement with the crescent shapes of bands of dye observed in transparent channels.Column efficiency and resolution in flow-based separation systems such as chromatography and field-flow fractionation (FFF) depend intimately on flow profiles in these systems. Flow nonuniformities are always present and significantly influence separative performance. Short-range nonuniformities in flow cause nonequilibrium band broadening, while long-range nonuniformities lead to zone distortion and ad-ditional broadening. Optimal performance requires a careful consideration of both of these two classes of flow profile effects. In FFF, attention has focused almost entirely on the parabolic or near-parabolic flow profile existing in the thin gap between the two major channel walls. Not only is the sepa-ration process itself controlled by this (short-range) profile but nonequilibrium effects, the major source of band broad-ening, are also related directly to the profile detail. Only recently have theoretical efforts been focused on long-range flow nonuniformities in FFF (1, 2). These nonu-niformities are considered here to be ones in which velocity differences are so widely spaced that diffusion is unable to transfer sample particles back and forth effectively between points of nonuniformity in the course of a run. Because of slow liquid-phase diffusion, distances of 1 mm or greater must generally be considered long range. Flow nonuniformities over the breadth (the span from one edge to another) of an FFF channel, involvingtypically a distance of a centimeter or more, are clearly in the long-range class. Two sources of flow nonuniformity along the breadth di-mension have been identified. The first arises at the channel